Are you trying to destroy the big ships or the fighters? The basic fighters in the easy missions should only take a couple of hits to kill. A frigate on the other hand, you can only kill the turrets most of which are a bit harder than a fighter, the main turret on the front is significantly harder to kill. You can also take out their engines with a bit of effort. On Destroyers and up, you can only really take out turrets and shield generators (if they have them, in which case they need to be taken out first).

Frigate has four turrets at the front, two in the middle, two at the back as well as two other targetable areas that I've never killed.
Destroyer has three rows of four turrets on the top and the same on the bottom, I also seem to remember a cluster of four turrets amidships on top. can also have four shield generators on the back part of the topside, also has a bridge, which again I have never been able to destroy.